Method of performing fingerprint matching

ABSTRACT

The method of performing fingerprint matching includes a matching algorithm that combines affine moment invariants (AMIs) and translation, rotation and scaling invariants (TRS) based on moments analysis without requiring minutiae detection. Preprocessing normalizes the fingerprint image using the Federal Bureau of Investigation&#39;s wavelet scalar quantification (WSQ) compression standard definition. Analysis of the orientation field reliably and accurately determines the reference point. The area within a predetermined range around the detected reference point is used as a region of interest (ROI) for feature extraction. A directional filter bank transform (DFB) obtains directional components of the image. An invariant moment analysis on sub-bands of the filtered images extracts features while limiting the effects of noise and non-linear distortions. Absolute distance is used to match the fingerprints.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to computerized methods forprocessing images, and particularly to a method of performingfingerprint matching having an algorithm based on matching that combinesdirectional features with moment invariants.

2. Description of the Related Art

Fingerprint matching techniques can be cast into four broad classes,namely, minutiae, correlation, Ridge features (texture), andTransform-based techniques. However, considering the types ofinformation used, a method can be broadly categorized as minutiae-basedor texture-based. While minutiae-based fingerprint verification systemshave shown high accuracy, they ignore the rich information in ridgepatterns, which can be useful to improve matching accuracy.

Texture-based fingerprint matching techniques include those that usefingerprint ridge features. Methods exist that estimate the nonlineardistortion in fingerprint pairs based upon ridge curve correspondences.

Exemplary prior art filter banks and directional filter banks employ afilter-based algorithm using a bank of Gabor filters. Gabor filters areused to capture local and global details of a fingerprint into a fixedfinger code. Fingerprint matching is then performed using the Euclideandistance between two corresponding finger codes.

Another approach, which is based on DFB filtering, decomposes thefingerprint image into eight directional sub-band outputs. This createsa frequency decomposition of the input and output that can be used tocreate a filtered image output. Directional energy distributions foreach block are then extracted from the decomposed sub-bands. To reducenoise effect and improve efficiency, only dominant directional energycomponents are kept as elements of the input feature vector. Additionalinput feature vectors in which various rotations are considered areextracted, and these input feature vectors are compared with an enrolledtemplate feature vector.

The aforementioned texture and transform-based matching methods haveadvantages dealing with such images, as they utilize features that arenot based solely on minutiae templates. However, it should be noted thatone main advantage of minutiae-based approaches is that they are faster.There remains a need for a fast texture and transform-based matchingmodel.

Thus, a method of performing fingerprint matching solving theaforementioned problems is desired.

SUMMARY OF THE INVENTION

The method of performing fingerprint matching includes a matchingalgorithm that combines affine moment invariants (AMIs) withtranslation, rotation and scaling invariants (TRS), and is based onmoments analysis without requiring minutiae detection. Preprocessingnormalizes the fingerprint image using the Federal Bureau ofInvestigation's wavelet scalar quantification (WSQ) compression standarddefinition. Analysis of the orientation field reliably and accuratelydetermines the reference point. The area within a predetermined rangearound the detected reference point is used as a region of interest(ROI) for feature extraction. A directional filter bank transform (DFB)obtains directional components of the image. An invariant momentanalysis on sub-bands of the filtered images extracts features, whilelimiting the effects of noise and non-linear distortions. Absolutedistance is used to match the fingerprints.

These and other features of the present invention will become readilyapparent upon further review of the following specification anddrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is an input frequency partition map used in a method ofperforming fingerprint matching according to the present invention.

FIG. 1B is a sub-band output used in a method of performing fingerprintmatching according to the present invention.

FIG. 1C is an exemplary fingerprint image.

FIG. 1D is a sub-band outputs decomposition using 8-band DFB in a methodof performing fingerprint matching according to the present invention.

FIG. 2 is a flowchart of a method of performing fingerprint matchingaccording to the present invention.

FIG. 3A is an original image block used in a method of performingfingerprint matching according to the present invention.

FIG. 3B are sub-band output blocks used in a method of performingfingerprint matching according to the present invention.

FIG. 4 shows a reference point on the convex ridge used in a method ofperforming fingerprint matching according to the present invention.

FIG. 5 is a sample fingerprint used to explain features of a method ofperforming fingerprint matching according to the present invention.

FIG. 6 is an ROI (region of interest) of the sample fingerprint of FIG.5.

FIG. 7 is a sample fingerprint used to explain features of a method ofperforming fingerprint matching according to the present invention.

FIG. 8 is an ROI of the sample fingerprint of FIG. 7.

Similar reference characters denote corresponding features consistentlythroughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The method of performing fingerprint matching includes a matchingalgorithm summarized in the flowchart 200 shown in FIG. 2 that combinesaffine moment invariants (AMIs) with translation, rotation and scalinginvariants (TRS), and is based on moments analysis without requiringminutiae detection. Preprocessing normalizes the fingerprint image usingthe Federal Bureau of Investigation's wavelet scalar quantification(WSQ) compression standard definition. This matching algorithm includessteps 202 through 212, comprising acquiring an input fingerprint image202, detecting a reference point of the image 204, establishing a regionof interest around the detected reference point 206, using a filter bankto obtain directional components of the image 208, extractingfingerprint features using moment invariants 210, and comparing thefingerprint using a Euclidean distance measurement against a referencefingerprint 212.

Analysis of the orientation field reliably and accurately determines thereference point. The area within a predetermined range around thedetected reference point is used as a region of interest (ROI) forfeature extraction. A directional filter bank transform (DFB) obtainsdirectional components of the image.

An invariant moment analysis on sub-bands of the filtered imagesextracts features, while limiting the effects of noise and non-lineardistortions. Absolute distance is used to match the fingerprints.

A fingerprint consists of a series of ridges that mainly flow parallelto the locally dominant direction and occasionally make localsingularities, like a core or delta point. Since fingerprint patternshave strong directionality, directional information can be exploited asfingerprint features. In this sense, a DFB is suitable for extractingthe features of fingerprints containing many linear and directionalcomponents because it can effectively and accurately decompose an imageinto several directional sub-band outputs.

The DFB basically consists of low pass filters (H₀), quincunx downsamplers (Q) (a quincunx is five coplanar points, four of the pointsdefining a rectangle or square, the fifth point being in the center),diamond conversion matrices (R), modulators (e^(−jω1π)), andpostsampling matrices (B). The modulator varies the spectrum of theimage so that the modulated image can be divided into two directionalsub-band images by a low pass filter with a diamond-shaped pass-band.Meanwhile, the quincunx down sampler simultaneously down samples theimage and rotates it by 45°.

The input is modulated, filtered, and downsampled, resulting in twosub-band images. Then the two sub-hand images are further divided intofour sub-band images using a procedure similar to that used in the firststep. In the final phase, diamond conversion matrices are required totransform the parallelogram-shaped pass-band into one with a diamondshape. These diamond conversion matrices enable the DFB to beimplemented using only a one-dimensional (1-D) filter prototype.Postsampling matrices are then appended to the end of the filter bank toremove the phenomenon of frequency scrambling, resulting from thefrequency shift due to the modulator and non-diagonality of the overalldown sampling matrix. Filter bank stages can be implemented in aseparable polyphase form to achieve highly efficient realizations. Then,eight directional sub-band outputs are generated.

The method of performing matching identification uses a DFB structureknown by artisans of ordinary skill. However, the design of the low passfilters is achieved through a linear phase IIR (Infinite ImpulseResponse) filter. As a result of the downsampling, the eight-banddecompositions are rectangular. The analysis stage is based on athird-order decomposition of N×N images, leading to eight sub-bandswhere the first half of the sub-bands has a size of N/4×N/2, while theother half has a size of N/2×N/4, respectively.

The method of performing fingerprint matching also contemplates the useof curvelet basis functions. The curvelet transform is obtained byfiltering and then applying windowed ridgelet transforms on eachbandpass image. This is done by sub-band decomposition of the objectinto sequences of sub-bands. After that, each sub-band is windowed intoblocks of appropriate size, depending on its center frequency. Finally,ridgelet transforms will be applied on windowed blocks. Therefore,curvelet basis functions can be viewed as a local grouping of waveletbasis functions into linear structures so that they can capture thesmooth discontinuity curve more efficiently.

Some properties of the fingerprints include directional components.Directional components may be characterized mathematically by a gradientG_(mn), as defined in equation (1), and corresponding angle θ_(mn), asdefined in equation (2), as follows:G _(min) =M×(|G _(mn) ^(x) |+|G _(mn) ^(y)|)  (1)θ_(mn)=tan⁻¹ [G _(mn) ^(y) /G _(mn) ^(x)]  (2)

A local dominant orientation estimate is then defined by equation (3):

$\begin{matrix}{\rho_{mn} = \frac{\sum\limits_{{({i,j})} \in w}{G_{ij}{\cos\left( {\theta_{mn} - \theta_{{ij})}} \right.}}}{\sum\limits_{{({i,j})} \in w}G_{ij}}} & (3)\end{matrix}$

Dominant local orientation θ is defined as:

$\begin{matrix}{\theta = {{\frac{1}{2}{\tan^{- 1}\left\lbrack \frac{\sum\limits_{m = 1}^{M}{\sum\limits_{n = 1}^{N}{\rho_{mn}^{2}{\sin\left( {2\theta_{mn}} \right)}}}}{\sum\limits_{m = 1}^{M}{\sum\limits_{n = 1}^{N}{\rho_{mn}^{2}{\cos\left( {2\theta_{mn}} \right)}}}} \right\rbrack}} + \frac{\pi}{2}}} & (4)\end{matrix}$

With respect to directional filter bank analysis of the fingerprintwhere the input image is analyzed into directional sub-band images, eachdirectional block may have a directional energy defined as:E _(k)(I,J)=Σ_(i=0) ^(m) ^(k) Σ_(j=0) ^(n) ^(k) |f _(k)(I,J;i,j)|  (5)

A direction based on gradient-based methods and filtered for noise isdefined by equation (6):

$\begin{matrix}{{{d\left( {I,J} \right)} = m},{{if}\mspace{14mu}{\underset{m}{Maximize}\left\lbrack {E_{m}\left( {I,J} \right)} \right\rbrack}}} & (6)\end{matrix}$

Recognizing patterns in images has three main approaches: brute force,image normalization and invariant features. Brute force requires the useof all possible representations of images, which include their rotated,scaled, blurred and deformed versions.

This method will have a very high time complexity, which is notdesirable. The image normalization approach transforms the image into astandard position, which requires the solving of difficult inverseproblems that are ill-posed or ill-conditioned.

The invariants approach uses a set of measurable quantities that areinsensitive to particular deformation. Those invariant features haveenough discriminating power to distinguish patterns into differentclasses. Mathematically speaking, selected features have the propertycalled invariance, which can be expressed as:I(f)=I(D(f))  (7)

That is, invariant I is a function that does not change its value underdegradation operator D. Invariants have different categories based ondifferent points of view, and can be categorized based on the type ofinvariance, namely, translation, rotation, scaling, affine, projective,and elastic geometric invariants. They may also be categorized based onradiometric invariants, which exist with respect to linear contraststretching, nonlinear intensity transformers, and convolution. Moreover,the linear invariants may be categorized based on mathematical tools,such as a simple shape descriptor, like compactness, convexity,elongation, etc. Transform coefficient features, such as Fourier,wavelet, and Hadamard descriptors, such as Point set invariants, whichuse positions of dominant points, or differential invariants, which usederivatives of the object boundary, are also linear invariantcategories. Moment invariants use special functions of image moments.

Categories may also be based on the part of the object needed tocalculate the invariant, such as global invariants, which are calculatedfrom the whole image, or local invariants, which are calculated fromdominant points. Semi-local invariants use properties from both globaland local invariants.

Moments are scalar quantities used to characterize a function and tocapture its significant features, and used in statistics for describingthe shape of a probability density function. Mathematically speaking,moments are “projections” of a function onto a polynomial basis.

Broadly speaking, moments are categorized, according to the polynomialbasis used, into geometric and complex moments, and orthogonal moments.In the image processing field, a moment is a certain particular weightedaverage of the image pixel intensities, or a function of such moments,usually chosen to have some attractive property or interpretation. Imagemoments are useful to describe objects after segmentation. Simpleproperties of the image that are found via image moments include area,intensity, centroid, and information about its orientation.

The geometric moments of the 2-D continuous function f(x,y), with astandard power basis k_(pq)(x,y)=x^(p)y^(q) is defined by:M _(pq)=∫_(−∞) ^(∞)∫_(−∞) ^(∞) x ^(p) y ^(p) f(x,y)dxdy for p, q=0, 1,2, . . . , n  (8)

Adapting the above equation to scalar (grayscale) image with pixelintensities I(x,y), raw image moments are calculated by:M _(ij)Σ_(x)Σ_(y) x ^(i) y ^(i) I(x,y)  (9)

Complex moments are based on the polynomial basisk_(pq)(x,y)=(x+iy)^(p)=(x−iy)^(q) and are defined by:c _(pq)=∫_(−∞) ^(∞)∫_(−∞) ^(∞)(x+iy)^(p)(x−iy)^(q) f(x,y)dxdy  (10)

Orthogonal (OG) moments are preferred in the literature because they area fast and stable numerical implementation. Another reason why OGmoments are used is due to better image construction. A 2D polynomialorthogonal on a rectangle is constructed as products of 1D OGpolynomials p_(k)(x). The OG moments will have the form:v _(pq) =n _(p) n _(q)∫_(Ω) p _(p)(x)p _(q)(y)f(x,y)dxdy  (11)where n_(p), n_(q) are some normalized factors and Ω is the area oforthogonality. The image f(x,y) should be scaled such that its supportis contained in Ω.

The method of performing fingerprint matching preferably usestranslation, rotation and scaling invariants (TRS). Thus, momentfeatures are favored because their features can provide the propertiesof invariance to scale, position, and rotation. For a 2-D continuousfunction f(x,y), the moment of order (p+q) is defined as:m _(pq)=∫_(−∞) ^(∞)∫_(−∞) ^(∞) x ^(p) y ^(q) f(x,y)dxdy for p, q=0, 1,2, . . . , n  (12)

The central moments are defined as:

$\begin{matrix}{{\mu_{pq} = {\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{\left( {x - x_{c}} \right)^{p}\left( {y - y_{c}} \right)^{q}{f\left( {x,y} \right)}{\mathbb{d}x}{\mathbb{d}y}}}}}{{where},}} & (13) \\{x_{c} = {{\frac{m_{10}}{m_{00}}\mspace{14mu}{and}\mspace{14mu} y_{c}} = \frac{m_{01}}{m_{00}}}} & (14)\end{matrix}$

If f(x,y) is a digital image, then equation (13) becomes:μ_(pq)=Σ_(x)Σ_(y) x−x _(c))^(p)(y−y _(c))^(q) f(x,y)  (15)

Invariance is obtained by proper normalization of each moment. Inprinciple, any moment can be used as a normalizing factor, provided thatit is nonzero for all images in the experiment. Since low-order momentsare more stable to noise and easier to calculate, we normalize mostoften by a proper power of μ₀₀ as follows:

$\begin{matrix}{{v_{pq} = \frac{\mu_{pq}}{\mu_{00}^{w}}}{{where},}} & (16) \\{w = {\frac{p + q}{2} + 1}} & (17)\end{matrix}$

The moment v_(pq) is called normalized central geometric moment. Notethat the moment that was used for scaling normalization can no longer beused for recognition because the value of the corresponding normalizedmoment is always one.

Affine moment invariants (AMIs) play a very important role inmoment-based pattern recognition applications. They are invariant withrespect to affine transform of the spatial coordinates. Affinetransformation is a general linear transform of spatial coordinates ofthe image, which can approximate the projective transform.

The theory of AMIs is closely connected to the theory of algebraicinvariants, and the Fundamental theorem describes this connection. Thealgebraic invariant is a polynomial of coefficients of a binary form,whose value remains the same after an affine transform of thecoordinates. In the theory of algebraic invariants, only the transformswithout translation are considered. Let us consider an image f and twoarbitrary points (x_(i),y_(l)), (x₂,y₂) from its support. Let us denotethe “cross-product” of these points as C₁₂:C ₁₂ =x ₁ y ₂ −x ₂ y ₁  (18)

After an affine transform, it holds that:C ₁₂ =J·C ₁₂,  (19)which means that C₁₂ is a relative affine invariant. Various numbers ofpoints are considered and their cross products integrated on the supportof f. These integrals can be expressed in terms of moments and, afterproper normalization, they yield affine invariants.

Mathematically, having r points (r≧2) A functional I is defineddepending on r and on non-negative integers n_(kj), as:I(f)=∫_(−∞) ^(∞)∫_(−∞) ^(∞)

_(k,j=1) ^(r) C _(kj) ^(n) ^(kj) ·Π_(i=1) ^(r) f(x _(i) ,y _(i))dx _(i)dy _(i)  (20)Note that it is meaningful to consider only j>k because C_(kJ)=−C_(jk)and C_(kk)=0. After an affine transform, I(f) becomes:I(f)′=j ^(W) |J| ^(r) ·I(f)  (21)where w=Σ_(k,j)n_(kj) is called the weight of the invariant and r iscalled the degree of the invariant. If I(f) is normalized by μ₀₀ ^(w+r),a desirable absolute affine invariant is obtained:

$\begin{matrix}{\left( \frac{{I(f)}^{\prime}}{\mu_{00}^{w + r}} \right) = \left( \frac{I(f)}{\mu_{00}^{w + r}} \right)} & (22)\end{matrix}$

The maximum order of moments of which the invariant is composed iscalled the order of the invariant. The order is always less than orequal to the weight.

An important note here is that we can generate as many invariants as wewish but only a few of them are independent since dependent invariantsare useless in practice, in the sense that they do not increase thediscrimination power of the recognition system at all while increasingthe dimensionality of the problem. This leads to growth of thecomplexity and even to misclassifications.

There might be various kinds of dependency in the set of all AMIs. Theycan be categorized into five groups: (1) Zero invariants: Some AMIs maybe identically zero regardless of the image from which they arecalculated. (2) Products: Some invariants may be products of otherinvariants. (3) Linear combinations: Some invariants may be linearcombinations of other invariants. (4) Identical invariants. (5)Polynomial dependencies: if there exists a finite sum of products ofinvariants (including their integer powers) that equals zero, theinvariants involved are polynomially dependent.

The invariants having the dependencies (1) to (4) are called reducibleinvariants. After eliminating all of them, a set of so-calledirreducible invariants is obtained. However, irreducibility does notmean independence. Eighty independent invariants (AMIs up to the weight12) out of 1589 irreducible invariants are used by the method ofperforming fingerprint matching.

For feature extraction, the original fingerprint image is decomposedinto eight directional sub-band outputs using the DFB. The momentinvariants to translation, rotation, and scaling and affine momentinvariants (independent and irreducible) of each block can be obtainedfrom the decomposed sub-band outputs. Let f₀(x, y) denote thecoefficient at position (x, y) of sub-band B corresponding to a regionof interest (ROI) of image block B, where θε{, 1, 2, . . . . , 7} forthe sub-bands.

For an N×N image, the first half of the eight sub-band outputs isN/4×N/2 in size, while the other half is N/2×N/4. Therefore, thesub-bands corresponding to an m×n block have size m/4×n/2 for directions0 to 3, and size m/2×n/4 for directions 4 to 7, as illustrated in theoriginal image block diagram 302 of FIG. 3A and the sub-band outputblock diagram 304 of FIG. 3B.

The proposed scheme of feature extraction first locates a referencepoint and establishes an ROI around the detected reference point. Theestablished ROI is then decomposed into eight directional sub-bandoutputs using a DFB.

Finally, the fingerprint feature values based on moment invariants (TRS& AMIs) are calculated from each sub-block of the decomposed sub-bandoutputs.

With respect to image normalization, the objective is to decrease thedynamic range of the gray between ridges and valleys of the image. Wenormalize the image to constant mean and variance. Normalization is doneto remove the effects of sensor noise and finger pressure difference.Let I(I,j) denote the gray value at pixels (i,j). M and VAR are theestimated mean and variance of the input fingerprint image. We use theFBI WSQ standard for gray scale images:

$\begin{matrix}{{{I^{\prime}\left( {i,j} \right)} = \frac{{I\left( {i,j} \right)} - M}{{VAR}^{\prime}}},} & (23)\end{matrix}$where VAR′=VAR/128 for 8 bits of precision per pixel. As shown in FIG.4, the fingerprint 400 has a reference core point 402, which is definedas the point of the maximum curvature on the convex ridge and is usuallylocated in the central area of a fingerprint, such as fingerprint 400. Asummary of reference point location algorithm is presented below. (1)Estimate the orientation field O using a window size of w×w. (2) Smooththe orientation field in a local neighborhood. Let the smoothedorientation field be represented as O′. In order to perform smoothing(low-pass) filtering, the orientation image needs to be converted into acontinuous vector field, which is defined as:φ_(x)(i,j)=Σ_(u=−w) _(φ) _(/2) ^(w) ^(φ) ^(/2)Σ_(v=−w) _(φ) _(/2) ^(w)^(φ) ^(/2) W(u,v)·φ_(x)(i−uw,j−vw)  (24)φ_(y)(i,j)=Σ_(u=w) _(φ) _(/2) ^(w) ^(φ) ^(/2)Σ_(v=w) _(φ) _(/2) ^(w)^(φ) ^(/2) W(u,v)·φ_(y)(i−uw,j−vw)  (25)where W is a two-dimensional low-pass filter with unit integral andw_(φ)×w_(φ) specifies the size of the filter. (3) Compute ε, an imagecontaining only the sine component of O′. (4) Initialize A, a labelimage used to indicate the reference point. (5) For each pixel (i j),integrate pixel intensities (sine component of the orientation field).(6) Find the maximum value and assign its coordinate as the referencepoint.

After determining the coordinates of the reference point, we crop thefingerprint image into an ROI. In order to speed up the overall process,we use only a predefined square area (ROI) with size N×N around thereference point at the center for feature extraction, instead of usingthe entire fingerprint. In our experiment, we set N to 192. FIGS. 5 and6, and FIGS. 7 and 8 demonstrate the ROI centered on the determinedreference point of two input fingerprints, respectively. As shown inFIGS. 5 and 6, the center of the cropped image 600 (FIG. 6) centers theposition of the reference point 502 of fingerprint 500 (FIG. 5), whoseROI is established within the image. As shown in FIGS. 7 and 8, thecenter of the cropped image 800 (FIG. 8) centers the position of thereference point 702 of fingerprint 700 (FIG. 7), whose ROI exceeds theimage bound.

In case the detected reference point is located at the corner of theimage, as shown in FIG. 8, establishing the ROI of a fingerprint exceedsthe bound of an image. In such a case, the method of performingfingerprint matching sets up the ROI by inserting zeros in the outsidearea of the image. The ROI area with zero value is excluded whenfingerprint features are calculated and matching is performed. At thisstage, invariant moment analysis is applied on each one of the eightsub-bands, respectively.

As shown in FIGS. 1A, 1B, 1C, and 1D, the extracted ROI is decomposedinto eight directional sub-band outputs. This procedure is accomplishedby the use of an eight-band DFB. As most clearly shown in frequencypartition map 100 and sub-band output diagram 103, it should be notedthat each sub-band is divided into sub-blocks, and a set of 35independent AMIs and 21 TRS moment invariants of the 5th order arecomputed for each sub-block. As a result 56 sets of invariant momentsfor each of the 8 sub-blocks are extracted as features to represent afingerprint (see the decomposed sub-band outputs 107 of FIG. 1D, whichhave been decomposed from print image 105, shown in FIG. 1C.

The procedure for feature extraction can be summarized as follows. (1)Normalize the image. (2) identify the core point and extract the ROI.(3) Apply the eight-band DFB to the ROI with dimension N×N. The outputis a set of eight sub-bands. (4) Further divide each sub-hand outputinto sub-blocks that will serve as the region of support for the featurevector calculations. If we envision a sub-block of size n×n (where N isa multiple of n) then the sizes of the corresponding sub-blocks with thesub-bands are n/4×n/2 for sub-bands 0 to 3 and n/2×n/4 for sub-bands 4to 7. (5) Calculate the 56 set of invariant moments from each “smallerblock” to form a feature vector, as discussed above. (6) Finally,combine the features calculated from each sub-block i_(θk) into onevector, V_(f)={I_(θ1), I_(θ2), . . . , I_(θk)}, where θε{0, 1, 2, 3, 4,5, 6, 7} and kε{0, 1, 2, . . . , 56}.

With respect to fingerprint matching, generally speaking, other methodsrequire that before the input print and template print are compared witheach other, they should be translationally and rotationally aligned witheach other. Rotational alignment is achieved by generating cyclicalinput feature vectors and matching input feature vectors with templatefeature vectors. In the method of performing fingerprint matching, thetranslational alignment is not of concern because invariant analysis isapplied to the extracted ROI by the reference point detection process.Since the feature extraction process is based on moments that areinvariant to translation, rotation and scaling, the proposed method isrobust to angular deviations without rotation and translationcompensation.

Fingerprint matching is performed based on finding the absolute distancebetween the input feature vectors and the template feature vectorenrolled in the database. Let:V _(f1) ={a ₁ , a ₂ , . . . , a _(n)} and V _(f2) {b ₁ , b ₂ , . . . , b_(n)}  (26)Denoting the feature vectors of the two fingerprints to be matched, thedifference vector V_(d) of the two fingerprint feature vectors iscalculated as in (27).

$\begin{matrix}{V_{d} = \left( {\frac{{a_{1} - b_{1}}}{\max\left( {a_{1},b_{1}} \right)},{\frac{{a_{2} - b_{2}}}{{\max\left( {a_{2},b_{2}} \right)},}\mspace{14mu}\ldots\mspace{14mu}\frac{{a_{n} - b_{n}}}{\max\left( {a_{n},b_{n}} \right)}}} \right)} & (27)\end{matrix}$The absolute distance of the two matching vectors is defined as in (28).

$\begin{matrix}{R_{m} = {\sum\limits_{i = 1}^{n}\frac{{a_{i} - b_{i}}}{\max\left( {a_{i},b_{i}} \right)}}} & (28)\end{matrix}$

It will be understood that the diagrams in the Figures depicting themethod of performing fingerprint matching are exemplary only, and may beembodied in a dedicated electronic device having a microprocessor,microcontroller, digital signal processor, application specificintegrated circuit, field programmable gate array, any combination ofthe aforementioned devices, or other device that combines thefunctionality of the method of performing fingerprint matching onto asingle chip or multiple chips programmed to carry out the method stepsdescribed herein, or may be embodied in a general purpose computerhaving the appropriate peripherals attached thereto and software storedon non-transitory computer readable media that can be loaded into mainmemory and executed by a processing unit to carry out the functionalityof the apparatus and steps of the method described herein.

It is to be understood that the present invention is not limited to theembodiments described above, but encompasses any and all embodimentswithin the scope of the following claims.

We claim:
 1. A computer-implemented method of performing fingerprintmatching, comprising the steps of: acquiring a first fingerprint image;locating a reference core point within the first fingerprint image inorder to initiate feature extraction of the first fingerprint image;establishing a region of interest (ROI) around the reference core point;decomposing the region of interest into eight separate directionalsub-band outputs; calculating translation, rotation, and scaling (TRS)independent moment invariants and affine moment invariants from each ofthe eight separate directional sub-band outputs by: calculating at leastone geometric moment invariant M_(pq), said geometric moment invariantcalculation being defined by the relation M_(pq)=∫_(−∞) ^(∞)∫_(−∞)^(∞)x^(p)y^(q)f(x,y)dxdy for p, q=0, 1, 2, . . . , n, where n representsa number of stored template features, x and y are Cartesian coordinates,and f(x,y) is a continuous function; adapting the geometric momentinvariant calculation to grayscale images having pixel intensitiesI(x,y), the geometric moment invariant calculation adaptation beingcharacterized by the relation M_(Ij)=Σ_(x)Σ_(y)x^(I)y^(j)I(x,y) forI,j=0, 1, 2, . . . , n; calculating at least one complex momentinvariant c_(pq), the complex moment invariant calculation being definedby the relation c_(pq)=∫_(−∞) ^(∞)∫_(−∞)^(∞)(x+iy)^(p)(x−iy)^(q)f(x,y)dxdy, where i is the complex number, theat least one complex moment invariant being based on a polynomial basisk_(pq)characterized by the relation k_(pq)(x,y)=(x+iy)^(p)(x−iy)^(q);and calculating at least one orthogonal moment v_(pq), the orthogonalmoment invariant calculation being defined by the relationv_(pq)=n_(p)n_(q)∫∫_(Ω)p_(p)(x)p_(q)(y)f(x,y)dxdy, wherein n_(p)andn_(q) are normalized factors and Ω is an area of orthogonality, thegrayscale image being scaled such that its support is contained in Ω;combining features calculated from each of the separate directionalsub-band outputs into a first feature vector V_(f) characterized by therelation V_(f)={I_(θ1), I_(θ2), . . . , I_(θk)}, where θε{0, 1, 2, 3, 4,5, 6, 7}, corresponding to the eight separate directional sub-bandoutputs, k ε{0, 1, 2, . . . , 56}, corresponding to the independentmoment invariants from each of the eight separate directional sub-bandoutputs, and I_(θk)is a feature sub-block of the θ-th directionalsub-band and the k-th independent moment invariant; calculating anabsolute distance between the first feature vector and a second vectorV_(f2)including features of a second fingerprint having similarlyobtained moment invariants, the second vector being characterized by therelation V_(f2)={b₁, b₂, . . . , b_(n)}, where each of the {b₁, b₂, . .. , b_(n)}represent one of the n stored template features; anddisplaying match results based on the first and second fingerprintabsolute distance calculation step.
 2. The computer-implemented methodof performing fingerprint matching according to claim 1, wherein saidsteps of calculating TRS and calculating affine moment invariantsfurther comprise normalization of each of the moment invariants.
 3. Thecomputer-implemented method of performing fingerprint matching accordingto claim 1, wherein said step of calculating TRS and calculating affinemoment invariants further comprises the step of calculating at least onecentral moment invariant μ_(pq), the central moment invariantcalculation being defined by the relation μ_(pq)=∫_(−∞) ^(∞)∫_(−∞)^(∞)(x−x_(c))^(p)(y−y_(c))^(q)f(x,y)dxdy, wherein a digital imagerepresentation of g(x,y) characterizes μ_(pq) by the relationμ_(pq)=Σ_(x)Σ_(y)(x−x_(c))^(p)(y−y_(c))^(q)f(x,y), where${x_{c} = {{\frac{m_{10}}{m_{00}}\mspace{14mu}{and}\mspace{14mu} y_{c}} = \frac{m_{01}}{m_{00}}}},$where m_(pq) represents a moment of order for p,q=0, 1, 2, . . ., n. 4.The computer-implemented method of performing fingerprint matchingaccording to claim 3, wherein said step of calculating TRS andcalculating affine moment invariants further comprises the step ofcalculating at least one absolute affine invariant, the at least oneabsolute affine invariant calculation being defined by the relation${\left( \frac{{I(f)}^{\prime}}{\mu_{00}^{w + r}} \right) = \left( \frac{I(f)}{\mu_{00}^{w + r}} \right)},$where I(f) is a function on (f), I(f)′ represents I(f)following anaffine transform thereon, w is a weight of the invariant, and rcomprises at least two points in a field of the image.
 5. Thecomputer-implemented method of performing fingerprint matching accordingto claim 4, wherein said normalization step further comprises using anFBI WSQ standard for gray scale images characterized by the relation${{I^{\prime}\left( {i,j} \right)} = \frac{{I\left( {i,j} \right)} - M}{{VAR}^{\prime}}},$where VAR′=VAR/128 for 8 bits of precision per pixel, where VAR is anestimated variance of the first fingerprint image and M is an estimatedmean of the first fingerprint image.
 6. The computer-implemented methodof performing fingerprint matching according to claim 5, wherein saidstep of locating of a reference core point further comprises the stepsof: estimating an orientation field O using a window size of w×w;converting an orientation of the first fingerprint image into acontinuous vector field (φ_(x) ,φ_(y)) characterized by the relationsφ_(x)(I,j)=Σ_(u=−w) _(φ) _(/2) ^(w) ^(φ) ^(/2)Σ_(v=−w) _(φ) _(/2) ^(w)^(φ) ^(/2)W(u,v)·φ_(x)(I−uw,j−vw) and φ_(y)(I,j)=Σ_(u=−w) _(φ) _(/2)^(w) ^(φ) ^(/2)Σ_(v=−w) _(φ) _(/2) ^(w) ^(φ)^(/2)W(u,v)·φ_(y)(I−uw,j−vw) thereby smoothing the orientation field ina local neighborhood, the smoothed orientation field being representedas O′, where W is a two-dimensional low-pass filter with unit integraland w_(φ)×_(φ) specifies a size of the filter; computing ε, an imagecontaining only the sine component of O′; initializing A, a label imageused to indicate the reference core point; integrating pixel intensitiesfor each pixel (i j) of the orientation field; finding a maximum valuepoint based on the pixel intensities integration; and assigningcoordinates of the maximum value point as the reference core point. 7.The computer-implemented method of performing fingerprint matchingaccording to claim 6, wherein said step of calculating an absolutedistance comprises the steps of representing the first feature vector bya set of n features, a₁, a₂, a₃ , . . . , a_(n) and computing aEuclidian distance R_(m) characterized by the relation$R_{m} = {\sum\limits_{i = 1}^{n}{\frac{{a_{i} - b_{i}}}{\max\left( {a_{i},b_{i}} \right)}.}}$